Question

1. multiply.

a) (4m + 1)(3m)
b) (2x - 3)(-4x)
c) (4.2n)(2n - 7)
d) (left( \frac{2}{3}m + 4
ight)(-9m))
e) (left( \frac{4}{3}x
ight)(6x - 12))

Explanation:

Step1: Multiply each term in the first bracket by the term in the second bracket.

For part a: \((4m + 1)(3m)=4m\times3m + 1\times3m\)

Step2: Simplify the products.

\(4m\times3m = 12m^{2}\) and \(1\times3m = 3m\), so \((4m + 1)(3m)=12m^{2}+3m\)

Step1: Multiply each term in the first bracket by each term in the second bracket.

For part b: \((2x - 3)(-4x)=2x\times(-4x)-3\times(-4x)\)

Step2: Simplify the products.

\(2x\times(-4x)=-8x^{2}\) and \(-3\times(-4x)=12x\), so \((2x - 3)(-4x)=-8x^{2}+12x\)

Step1: Multiply each term in the first bracket by each term in the second bracket.

For part c: \((4.2n)(2n - 7)=4.2n\times2n-4.2n\times7\)

Step2: Simplify the products.

\(4.2n\times2n = 8.4n^{2}\) and \(4.2n\times7 = 29.4n\), so \((4.2n)(2n - 7)=8.4n^{2}-29.4n\)

Step1: Multiply each term in the first bracket by each term in the second bracket.

For part d: \((\frac{2}{3}m + 4)(-9m)=\frac{2}{3}m\times(-9m)+4\times(-9m)\)

Step2: Simplify the products.

\(\frac{2}{3}m\times(-9m)=-6m^{2}\) and \(4\times(-9m)=-36m\), so \((\frac{2}{3}m + 4)(-9m)=-6m^{2}-36m\)

Step1: Multiply each term in the first bracket by each term in the second bracket.

For part e: \((\frac{4}{3}x)(6x - 12)=\frac{4}{3}x\times6x-\frac{4}{3}x\times12\)

Step2: Simplify the products.

\(\frac{4}{3}x\times6x = 8x^{2}\) and \(\frac{4}{3}x\times12 = 16x\), so \((\frac{4}{3}x)(6x - 12)=8x^{2}-16x\)

Answer:

a) \(12m^{2}+3m\)
b) \(-8x^{2}+12x\)
c) \(8.4n^{2}-29.4n\)
d) \(-6m^{2}-36m\)
e) \(8x^{2}-16x\)